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Last updated on December 2nd, 2024

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Square Root of 128

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Square root is the number obtained when a number is multiplied with itself. We apply the concept of square root in architecture, to measure volume and surface area. In this article, we’ll learn how to find the square root of 128.

Square Root of 128 for Omani Students
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What is the Square Root of 128

The square root of 128 is ±11.3137. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 128 is written as √128. 
 

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Finding the square root of 128

The different ways to find the square root of a number are prime factorization, long division  and approximation/estimation method.
 

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Square root of 128 using prime Factorization Method

The prime factorization of 128 breaks 128 into its prime numbers. 


The number 2 is the only prime number


Prime factorization of 128 is 27


Since 2 is repeating, we can pair them


Therefore, √128 is expressed as 23 x √2 →8√2, the simplest radical form.
 

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Square root of 128 using long division method

The long division method finds the square root of non-perfect squares.


Step 1: Write down the number 128


Step 2: Number 128 is a three-digit number, so pair them as (1), (28)


Step 3: Find the largest that is closest to the first pair (1), which is 12


Step 4: Write down 1 as the quotient, which will be the first digit of the square root.


Step 5: Subtracting 12  from 1 will leave zero as the remainder. Now bring down the second pair (28) and place it beside 0.


Step 6: Now double the quotient you have, that is add the quotient 1 with 1 and the result will be 2


Step 7: Choose a number such that it can be placed after 2 in the divisor. The two-digit number created should be less than the second pair (28). Here, we add 1 after 2, because the number formed will be less than 28.


Step 8: Subtract 21 from 28  → 28-21 =7. Now add a decimal point after the new quotient and adding two zeros will make it 700


Step 9: Apply step 7 over here and continue the process until you reach 0.


Step 10: We can write  √128 as 11.313.

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Square root of 128 by Approximation method

The approximation method finds the estimated square root of non-perfect squares.

 

Step 1: Identify the closest perfect square to 128. Numbers 121 and 144 are the closest perfect square to 128.


Step 2: We know that  √121 = 11 and  √144 = 12. Thus, we can say that  √128 lies between  11 and 12.


Step 3: Check if  √128 is closer to 11 or 12. Let us take 11.5 and 12. Since (11.5)2 is 132.25 and (12)2 is 144,  √119 lies between them.


Step 4: We can keep changing the values of 11.5 to 11. 6 and iterate the same process without changing 12 as the closest perfect square root.

 

The result of  √128 will be 11.313
 

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Common Mistakes and How to Avoid Them in Square Root of 128

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Square Root of 128 , Examples

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Problem 1

What is the value of “√128 × 2”?

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Explanation

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Problem 2

Which is larger, √128 or √144?

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Explanation

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Problem 3

The area of a square garden is 128 square feet. Calculate the length of one side.

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Explanation

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Problem 4

If a = √128, what is the value of a² + 8

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Explanation

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FAQs on 128 Square Root

1.Is 128 a cube root?

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2.What square numbers go into 128?

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3.What is 128 divisible by?

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4.What is the 4th root of 128?

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5.Is 128 divisible by 3?

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6.How does learning Algebra help students in Oman make better decisions in daily life?

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7.How can cultural or local activities in Oman support learning Algebra topics such as Square Root of 128?

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8.How do technology and digital tools in Oman support learning Algebra and Square Root of 128?

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9.Does learning Algebra support future career opportunities for students in Oman?

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Important Glossaries for Square Root of 128

  • Perfect Square: Product obtained when the same number gets multiplied twice

 

  • Approximate Value: Value closer to the exact number

 

  • Prime Factorization: Breaking down the number into its prime factors.
     
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About BrightChamps in Oman

At BrightChamps, we understand algebra as more than symbols—it’s a key to unlocking many opportunities! Our mission is to help children across Oman gain important math skills, focusing today on the Square Root of 128 with special attention to square roots—in an engaging, lively, and easy-to-follow manner. Whether your child is measuring how fast a roller coaster moves at Oman’s Dreamland Aqua Park, tracking local football scores, or managing their allowance for the latest gadgets, mastering algebra gives them confidence for everyday tasks. Our hands-on lessons make learning simple and fun. Because children in Oman learn differently, we adapt lessons to fit each learner’s style. From Muscat’s vibrant city life to beautiful natural landscapes, BrightChamps brings math to life, making it exciting throughout Oman. Let’s make square roots a joyful part of every child’s math journey!
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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